Graphene layer formation at low substrate temperature on a metal and carbon based substrate

ABSTRACT

A system and method for forming graphene layers on a substrate. The system and methods include direct growth of graphene on diamond and low temperature growth of graphene using a solid carbon source.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-In-Part of U.S. patent applicationSer. No. 13/481,110 filed May 25, 2012 and U.S. patent application Ser.No. 13/448,068, filed Apr. 16, 2012, U.S. Pat. No. 8652946, both ofwhich are incorporated herein by reference.

STATEMENT OF GOVERNMENT INTEREST

The U.S. Government claims certain rights in this invention pursuant toContract No. W-31-109-ENG-38 between the United States Government andthe University of Chicago and/or pursuant to DE-AC02-06CH11357 betweenthe United States Government and UChicago Argonne, LLC representingArgonne National Laboratory.

FIELD OF THE INVENTION

The invention relates generally to methods and systems for forminggraphene layers on a carbon based substrate. More particularly thisinvention relates to methods and systems for growth of graphene,including direct growth of graphene on diamond and low temperaturegrowth of graphene using a solid carbon source.

BACKGROUND OF THE INVENTION

Since the discovery of graphene and realization of its exceptionalelectronic properties in suspended form, there have been many efforts infabricating FET-type devices based on single and bilayer graphene on aSiO₂ substrate. However, performance of these devices is found to beinferior to the expected intrinsic properties of graphene. It has beenobserved that apart from carrier mobility in graphene, which issensitive to trapped charges, and surface impurities at thegraphene-oxide interlace, breakdown current density in graphene dependssensitively on the heat dissipation property of the underlyingsupporting substrate. Although graphene has extremely high intrinsicthermal conductivity, it is reported that in graphene devices that morethan 70% of the heat dissipates through the 300 nm SiO₂ on silicondirectly below the active graphene channel. The remainder of the heat iscarried to the graphene that extends beyond the device and metalliccontacts. Such a distribution of heat into the substrate causeundesirable effects on the overall performance of a device, such as thethermally generated carriers affecting the electronic mobilityparameters of a device fabricated on top of the substrate.

The breakdown current density measurements of multilayer and few layergraphene disposed on a SiO₂/Si substrate have been reported to be in therange of 7×10⁷ to 10⁸ A/cm². The main breakdown mechanism of graphene ismostly due to the Joule heating, which sensitively depends upon thethermal conductivity and surface roughness of the underlying substrate.The thermal conductivity of SiO₂ K=0.5-1.4 W/mK at RT is more than twoorders-of-magnitude smaller than that of Si, K=145 W/mK, which suggeststhat the use of a better heat-conducting material, directly belowgraphene, can improve graphene's JBR. Recently, it was demonstrated thatreplacement of SiO₂ with diamond-like carbon (DLC) helps tosubstantially improve the RF characteristics of the scaled graphenetransistors. However, DLC is an amorphous material with K=0.2-3.5 W/mKat room temperature (hereinafter “RT”), which is a very low value and isclose to that in SiO₂. Additionally, depending on the hydrogen content,the as deposited DLC films has high internal stress, which needs to bereleased by having to perform a separate step of annealing these filmsat higher temperatures (about 600° C.). These negative attributesprovide a very strong motivation for the search for other materialswhich can be used as substrates for graphene based devices.

SUMMARY OF THE INVENTION

In one embodiment conventional SiO₂ substrates are replaced withdiamond, such as synthetic single crystal diamond (“SCD”) hereinafterand a graphene layer. The problem of prior art systems concerning heatdissipation is substantially reduced, leading to an order of magnitudeincrease in breakdown current density (“JPR” hereinafter) reaching up toone thousand times improvement over conventional metal basedinterconnects in FET-type devices and other electronic deviceapplications like RF transistors. In other embodiments the substrate canbe ultranano crystalline diamond (“UNCD” hereinafter) with grain sizediameters of about5-10 nm, resulting in improving JPR about 50% ascompared to graphene on SiO₂ as a result of the increased thermalconductivity of the UNCD at elevated temperatures, close to thethermally-induced breakdown point.

In yet another embodiment a method and system provides direct growth ofgraphene layers on diamond, thereby eliminating various transferprocesses previously required. In this process the diamond substrate canbe single crystal or polycrystalline diamond.

In a further embodiment a method and system are provided for lowtemperature growth of graphene by using a solid carbon source andpreferably using a Ni surface as the substrate, thereby allowing singleor multilayer graphene in a controlled manner. In addition, the Ni (orother like performing transition metal or alloy) as the substrate isdeposited on an adhesion layer, such as Ti, or other well-knowncompatible adhesion layer material. The adhesion layer can then bedeposited on a substrate compatible with the adhesion layer. Such asubstrate can be Si, SiO₂, combination thereof, or other conventionaland compatible substrates to enable forming graphene by annealing adeposited polymer layer on the Ni or transition metal or metal alloylayer. Further, the polymer used to form the graphene can be a mixtureof aliphatic hydrocarbon an alkene hydrocarbon.

In yet another embodiment, a method relates to forming graphene byproviding a carbon precursor, forming a transition metal layer on thecarbon precursor, and dissolving the transition metal layer into thecarbon precursor by an annealing step at a temperature above 350 C.Then, the substrate is cooled below 1000 C thereby forming a graphenelayer on the carbon precursor in less than one minute.

Yet another embodiment relates to a method of forming graphene on asubstrate. A single crystal diamond substrate is provided. A transitionmetal layer is formed on the diamond substrate. The transition metallayer is dissolved into the diamond substrate by an annealing step. Thesubstrate is cooled to room temperature, thereby forming a graphenelayer.

Yet another embodiments relates to a method of forming graphene on asubstrate. A diamond substrate is provided. A transition metal layer isformed on the diamond substrate. The transition metal layer is dissolvedinto the diamond substrate by an annealing step. The substrate is cooledthereby forming a graphene layer from the diamond substrate as a carbonprecursor.

Yet another embodiment comprises providing a carbon precursor. Atransition metal layer is formed on the carbon precursor. The transitionmetal layer is dissolved into the carbon precursor by an annealing stepat a temperature above 350 C. The substrate is cooled to below 1000 C,thereby forming a graphene layer in less than one minute.

Yet another embodiment relates to a method of forming single domaingraphene on a substrate. A diamond substrate is provided. A transitionmetal layer is formed on the diamond substrate. At least one hole isformed in the transition metal layer and diamond substrate. Thetransition metal layer is dissolved into the diamond substrate by anannealing step. The substrate is cooled. Single domain graphene isformed suspended over the at least one hole.

Yet another embodiment relates to a method of forming graphene on asubstrate comprising providing a diamond substrate. A transition metallayer is formed on the diamond substrate. The transition metal layer isdissolved into the diamond substrate by an annealing step. The substrateis cooled, thereby forming a graphene layer from the diamond substrateas a carbon precursor.

Yet another embodiment relates to a method of forming patterned grapheneon a substrate comprising providing a diamond substrate. A transitionmetal is patterned on the diamond substrate. The transition metal isdissolved into the diamond substrate by an annealing step. The substrateis cooled, thereby selectively forming graphene exhibiting a graphenepattern corresponding to the patterned transition metal.

These and other advantages and features of the invention, together withthe organization and manner of operation thereof, will become apparentfrom the following detailed description when taken in conjunction withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic of a top-down fabrication method forproviding a graphene based device on a diamond substrate.

FIG. 2A illustrates an MPCVD system used to implement the schematicmethod of FIG. 1; FIG. 2B provides a schematic describing UNCD growth ina MPCVD system; FIG. 2C illustrates NEXAFS data for deposited UNCD thinfilms; FIG. 2D illustrates an AFM image of as grown UNCD; FIG. 2Eillustrates an AFM image of chemically/mechanically polished UNCD; FIG.2F illustrates Raman spectra of graphene on UNCD and separately for theUNCD substrate; and FIG. 2G illustrates Raman spectra of graphene on SCDand the SCD substrate.

FIG. 3A(1) illustrates a schematic of a two terminal device and FIG.3A(2) a three terminal device fabricated for testing an UNCD/Si and aSCD substrate; FIG. 3B illustrates an optical microscopy image of thetwo terminal graphene processing device/prototype interconnect on asingle crystal diamond; FIG. 3C illustrates an SEM image of the twoterminal graphene for producing an UNCD/Si device;' and FIG. 3Dillustrates a three terminal graphene for producing an UNCD/Si device.

FIG. 4A illustrates thermal resistance of an UNCD/Si substrate and areference Si wafer; FIG. 4B illustrates low field current voltagecharacteristics of a top gate graphene layer on a SCD device; FIG. 4Cillustrates source drain current for the three terminal graphene layerdeposited on an UNCD device as a function of top gate voltage bias; andFIG. 4D illustrates breakdown current density in the two dimensionalgraphene on UNCD and graphene layer on a SCD device.

FIG. 5 illustrates scaling of breakdown current density wherein J_(BR)is shown as a function of electrical resistance and length of grapheneinterconnects.

FIG. 6 illustrates a schematic diagram of process steps to obtain directgraphene growth on diamond.

FIG. 7A illustrates an SEM image of a diamond film covered withconformal graphene layer; and FIG. 7B illustrates Raman spectraconfirming growth of a few nm thick layer graphene on the diamond.

FIG. 8 illustrates a schematic of a graphene layer on a diamond/Sisubstrate;

FIG. 9 illustrates a gray scale plot of contrast as a function ofwavelength and diamond thickness with the gray scale contrast key on theright.

FIG. 10 illustrates contrast as a function of diamond thickness at afixed wavelength.

FIG. 11 illustrates thermal conductivity of Si wafers measured (squares)versus literature reported values (circles).

FIG. 12 illustrates thermal conductivity as a function of temperaturefor an UNCD/Si substrate and reference bulk Si.

FIG. 13A illustrates a schematic diagram of a first process step tosynthesize graphene on Ni at low temperature with a solid precursor;FIG. 13B illustrates a second process step of depositing a polymer layerin synthesizing graphene on Ni; and FIG. 13C illustrates a third processstep of graphene growth on Ni in synthesizing graphene on Ni.

FIG. 14A illustrates Raman spectra of graphene grown at 400° C.; FIG.14B shows an optical micrograph of a Ni surface supporting the grapheneof FIG. 14A; FIG. 14C shows Raman spectra of graphene grown at 500° C.on Ni; and FIG. 14D shows an optical micrograph of the Ni surfacesupporting the graphene of FIG. 14C.

FIGS. 15A-Billustrates wafer scale grown graphene on UNCD: FIG. 15A theRaman signature of graphene is demonstrated at different points of UNCDwafer covered with graphene; Figure B XPS analysis demonstrates clearcarbon C is signature, indicating no nickel remained on the surface andno oxygen originated defects.

FIGS. 16A-B illustrates in FIG. 16A SEM and AFM images of grown grapheneindicate the formation of the continuous uniform film with occasionalfolds occurring; FIG. 16B Raman signature of graphene films produces atdifferent temperatures indicates the variation in the number of grownlayers (single layer grown at 800° C. and multi-layer grown at 1000°C.). The Raman spectra of single layer graphene grown on copper and thentransferred on the UNCD film are provided for reference.

FIGS. 17A-E show lateral growth of single domain free-standing grapheneon diamond: FIG. 17A Successful growth of graphene on 4 holes ispresented; FIG. 17B full coverage of the hole is demonstrated; FIG. 17CGraphene partially grown on the hole confirms free-standing nature; FIG.17D TEM image confirms a single-domain graphene growth with FIG. 17ESAED pattern indicating diffraction of single-crystal film.

FIG. 18A Changes in the intensities of D and 2D peaks for Ramansignature of the graphene on the hole indicate growth of thefree-standing graphene; FIG. 18B. The Raman signature of graphene growndirectly on UNCD (outside area) is provided for the reference; FIG. 18CThe schematic of mechanism of free-standing graphene growth ispresented.

FIG. 19A-F show schematic of the Ni(111) facilitated graphene growth ispresented in FIGS. 19A-D with two mechanisms outlined by moleculardynamic (MD) simulations: FIG. 19E Carbon diffusion through the nickelfilm and eventual segregation of nickel through diamond grainboundaries, and FIG. 19F growth of uniform graphene film on Ni (111)surface. Carbon is presented by dark grey color, while nickel by orange.

FIG. 20 rapid thermal annealing process

FIGS. 21A-B shows a schematic of rapid thermal annealing process: FIG.21A indicates schematics and SEM cross-section of the initiallayer-by-layer film configuration, FIG. 21B demonstrates schematic andcross-section of the layer-by-layer film after annealing process.

FIG. 22 shows an AFM image of the single layer graphene transferred onSiO₂ substrate. Raman signature indicates single layer graphene withheight profile confirming the flake thickness of ˜0.6 nm.

FIGS. 23A-C show SEM images of the free-standing graphene growthprocedure: FIG. 23A Initial Ni/UNCD/Silicon configuration; FIG. 23B FIBpatterning to produce the hall in Ni/UNCD film; FIG. 23C lateral growthof graphene film over the hole after RTP annealing procedure.

FIGS. 24A-D show selective growth of graphene on diamond through nickelpatterning; FIGS. 24A and 24B demonstrate SEM images of graphene grownon diamond with selective growth of graphene also being confirmed withcorresponding Raman signatures of UNCD FIGS. 24C and graphene 24D.

FIG. 25 shows initial configuration showing a typical grain boundary(Σ13 twist (100)) in a ultra-nano-crystalline diamond (UNCD).

FIG. 26 Initial configuration showing the Ni(100) slab on top of theUNCD grain boundary.

FIG. 27 XRD analysis of 50 nm Ni film on UNCD wafer. The size of nickelcrystals is estimated from full width half maximum (fwhm) of Ni(111)peak (at 2θ=44.1) using Scherrer equation as 15 nm.

FIGS. 28A show the effect of orientation of the underlying Ni substrateon graphene growth. Snapshots of atomic configuration are shown atdifferent times during annealing of amorphous carbon deposited on Nisubstrates in our MD simulations; the Ni substrates are oriented withsurface normal along 111 (FIGS. 28A-D) and 001 (FIGS. 28E-H) directions,diring the annealing process, amorphous carbon undergoes orderingresulting in monolayer graphene sheet with nearly full coverage onNi(111), while graphene patches with significant number of holes anddefects are obtained on Ni(001); graphene growth on Ni(111) is favoreddue to the presence of close-packed triangular moiety of Ni atoms (FIG.28D) as compared to the square/rectangular arrangement of Ni atoms in001 plane (FIG. 28H).

FIG. 29 is an optical image of top-gated graphene device fabricated.Scale bar is 100 μm.

FIG. 30A Two terminal current-voltage characteristics Ids vs Vds at zerogate bias; FIG. 30B Three terminal measurement source-drain currentversus top-gate bias. Drain voltage is fixed at 0.1V.

FIG. 31 illustrates Fabrication of top-gate graphene FET on diamond. Thetop gate graphene FETs on UNCD with good charge carrier mobility of˜2000 cm²V⁻¹s⁻¹ for electrons and carrier density of ˜3.5×10¹² cm⁻²ismeasured at RT.

FIG. 32 illustrates a possible mechanism for the graphene growth ondiamond. It should be further appreciated that nanopatterning can bepossible using patterned nickel on UNCD.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In one embodiment graphene-based devices can be fabricated by a top-downmethodology to create graphene on a synthetic diamond substrate. Asshown in FIG. 1 a starting material 100 can be either single crystaldiamond or UNCD/NCD (“nanocrystalline diamond”) thin film deposited on asilicon substrate with a transferred graphene layer 110 on the top. Thenext step in the process is to spin coat a photoresist 120 followed bye-beam lithography 130 to pattern the graphene layer 110 and perform areactive ion etch (RIE) to transfer the pattern 140. The next step isdeposition of Au/Ti as metal contacts 150. A gate dielectric of HfO₂ 160is also deposited using an atomic layer deposition (hereinafter “ALD”)process for three terminal devices. Finally, a lift-off process is usedto etch away extra metal from unwanted regions. The final configurationof device 170 is as shown in a schematic displayed as an inset at theend of process flow-chart.

The UNCD films for this study were grown on Si substrates 165 in aconventional microwave plasma chemical vapor deposition (MPCVD) system175 at the Argonne National Laboratory (ANL). FIGS. 2A and 2B show theMPCVD system 175 used for the growth inside a cleanroom and schematic ofthe process, respectively. The growth conditions were altered to obtainlarger D, in the range 5-10 nm, instead of typical grain sizes D≈2-5 nmin UNCDs. This was done to increase K of UNCD without stronglyincreasing the surface roughness. We intentionally did not increase Dbeyond 10 nm or used MCD in order to keep δH in the range suitable forpolishing. The inset shows a 100-mm UNCD/Si wafer. Details of theoriginal growth process developed at ANL are described hereinafter.

The surface roughness of the synthetic diamond substrate 100 plays animportant role in reducing electron scattering at the graphene-diamondinterface 180 and increasing the electron mobility, μ. We performed thechemical mechanical polishing (hereinafter “CMP”) to reduce the as-grownsurface roughness from δH≈4-7 nm to below δH≈1 nm, which resulted in acorresponding reduction of the thickness, H, from the as-grown H≈1 μm to˜700 nm. The H value was selected keeping in mind conditions forgraphene visualization on UNCD together with the thermal managementrequirements (see Example I). The SCD substrates 100 were type IIb (100)grown epitaxially on a seed diamond crystal and then laser cut from theseed. For the graphene devices 170 fabrication, the SCD substrates 100were acid washed, solvent cleaned and put through the hydrogentermination process in a conventional manner. The near-edge rayabsorption fine-structure spectrum (NEXAFS) of the grown UNCD film 100confirms its high sp³ content and quality (FIG. 2C). The strongreduction of δH is evident from the atomic force microscopy (“AFM”hereinafter) images of the as grown UNCD and UNCD after CMP presented inFIGS. 2D and 2E, respectively. The surface treatment proceduresdeveloped for this study are described in the “Methods ” subsectionhereinafter.

The graphene and few-layer graphene (“FLG” hereinafter) were prepared byexfoliation from the bulk highly oriented pyrolytic graphite to ensurethe highest quality and uniformity. We selected flakes of therectangular-ribbon shape with the width W≧1 μm, which is larger than thephonon mean free path Λ˜750 nm in graphene. The condition W>Λ ensuredthat K does not undergo additional degradation due to the phonon-edgescattering, allowing us to study the breakdown limit of graphene itself.The length, L, of graphene ribbons was in the range of about 10-60 μm.We further chose ribbons with the small aspect ratio γ=W/L˜0.03-0.1 toimitate interconnects. Raman spectroscopy was used for determining thenumber of atomic planes, n, in FLG although the presence of sp² carbonat the grain boundaries in the UNCD 100 made the spectrum analysis moredifficult. FIG. 2F shows spectra of the graphene-on-UNCD/Si and UNCD/Sisubstrate. One can see a 1332 cm⁻¹ peak, which corresponds to theoptical vibrations in the diamond crystal structure. The peak isbroadened due to the small D in UNCD. The bands at ˜1170, 1500 and 1460cm⁻¹ are associated with the presence of trans-poly-acetylene and sp²phase at grain boundaries. The graphene G peak at 1582 cm⁻¹ and 2D bandat ˜2700 cm⁻¹ are clearly recognizable. FIG. 2G presents spectra of thegraphene-on-SCD, SCD substrate and difference between the two. Theintensity and width of 1332 cm⁻¹ peak confirms that we havesingle-crystal diamond.

In preferred embodiments the devices 170 were made of FLG with n≦5. FLGsupported on substrates or embedded between dielectrics preserves itstransport properties better than single layer graphene. Two-terminal(i.e., interconnects) and three-terminal (i.e., FETs) devices werefabricated on both UNCD/Si and SCD substrates. The electron-beamlithography (EBL) was used to define the source, drain contacts, andgate electrodes. The contacts consisted of a thin Ti film 200 covered bya thicker Au film 210. A top-gate HfO₂ dielectric layer 230 was grown bythe atomic layer deposition (“ALD” hereinafter). In a preferredembodiment as compared to a basic prior art graphene-on-SiO₂/Si devices,the gate electrode 220 and the graphene pad 110 were completelyseparated by the HfO₂ dielectric layer 230 to avoid oxide lift-off sharpedges, which can affect connection of the gate electrode 220. FIGS.3A(1) and (2) show schematics of the fabricated devices 170 withdetails. For testing the breakdown current density in FLG we usedtwo-terminal devices 230 in order to minimize extrinsic effects on thecurrent and heat conduction. Three-terminal devices 240 were utilizedfor μ mobility measurements. Conventional graphene-on-SiO₂/Si deviceswere prepared as references. FIG. 3B is an optical microscopy image of atwo terminal graphene-on-SCD device. FIGS. 3C and 3D show the scanningelectron microscopy (SEM) images of the two-terminal and three-terminalgraphene-on-UNCD devices, respectively.

In a preferred embodiment characterization was performed for >40 innumber of the graphene-on-diamond devices 170 and for >10 in number ofthe graphene-on-SiO₂/Si reference devices 170. To understand the originof the breakdown J_(BR) values were correlated with the thermalresistances of the substrates. The effective K of the substrates wasmeasured and their thermal resistance determined as R_(T)=H_(S)/K, whereH_(S) is the substrate thickness. For details of the thermalmeasurements see Example I. FIG. 4A shows thermal resistance, R_(T), forthe UNCD/Si and Si/SiO₂ (300-nm) substrates as a function of T. Notethat R_(T) for Si increases approximately linear with T, which isexpected because the intrinsic thermal conductivity of crystallinematerials decreases as K˜1/T for T above RT. The T dependence of R_(T)for UNCD/Si is notably different, which results from interplay of heatconduction in UNCD and Si. In UNCD, K grows with T due to increasinginter-grain transparency for the acoustic phonons that carry heat.UNCD/Si substrates, despite being more thermally resistive than Siwafers at RT, can become less thermally resistive at high T. TheR_(T)value for SCD substrate is ˜0.25×10⁻⁶ m²K/W, which is more thanorder-of-magnitude smaller than that of Si at RT. The thermal interfaceresistance, R_(B), between FLG and the substrates is R_(B)≈10⁻⁸ m²K/W,and it does not strongly depend on either n or the substrate material.For this reason, R_(B) does not affect the R_(T) trends.

FIG. 4B shows current-voltage (I-V) characteristics of graphene-on-SCDFET at low source-drain voltages for different top-gate, V_(TG), bias.The inset demonstrates a high quality of the HfO₂ dielectric and metalgate deposited on top of graphene channel. The linearity of I-Vsconfirms that the contacts are Ohmic. FIG. 4C presents the source-drain,I_(SD), current as a function of V_(TG) for graphene-on-UNCD FET. In thegood top-gate graphene-on-diamond devices the extracted μ was ˜1520cm²V⁻¹s⁻¹ for electrons and ˜2590 cm²V⁻¹s⁻¹ for holes. These mobilityvalues are acceptable for applications in downscaled electronics. InFIG. 4d we show results of the breakdown testing. For graphene-on-UNCD,we obtained J_(BR)≈5×10⁸ A/cm² as the highest value, while the majorityof devices broke at J_(BR)≈2×10⁸ A/cm². The referencegraphene-on-SiO₂/Si had J_(BR)≈10⁸ A/cm², which is consistent withconventional findings. The maximum achieved for graphene-on-SCD was ashigh as J_(BR)≈1.8×10⁹ A/cm². This is an important result, which showsthat via improved heat removal from graphene channel one can reach, andeven exceed, the maximum current-carrying capacity of ˜10 μA/nm² (=1×10⁹A/cm²) reported for CNTs. Without limiting the invention, the surprisingimprovement in J_(BR) for graphene-on-UNCD is explained by the reducedR_(T) at high T where the failure occurs. At this temperature, R_(T) ofUNCD/Si can be lower than that of Si/SiO₂ (see FIG. 4A).

The location of the current-induced failure spot and J_(BR) dependenceon electrical resistivity, ρ, and length, L, can shed light on thephysical mechanism of the breakdown. While not limiting the scope of theinvention, the failures in the middle of CNTs and J_(BR)˜1/ρ wereinterpreted as signatures of the electron diffusive transport, whichresulted in the highest Joule heating in the middle. The failures at theCNT-metal contact were attributed to the electron ballistic transportthrough CNT and energy release at the contact. There is a difference incontacting CNT with the diameter d˜1 nm and graphene ribbons 110 withW≧1 μm. It is easier to break CNT-metal than the graphene-metal contactthermally. In our study, we observed the failures both in the middle andnear the contact regions (see FIG. 5). The difference between these twotypes was less pronounced than that in CNTs. The failures occurred notexactly at the graphene-metal interface but on some distance, whichvaried from sample to sample. We attributed it to the width variationsin graphene ribbons leading to breakdowns in the narrowest regions, orin the regions with defects, which are distributed randomly. We did notobserve scaling of J_(BR) with ρ like in the case of CNTs.

J_(BR) for graphene scaled well with ρL, and FIG. 5 shows data forgraphene-on-UNCD with a similar aspect ratio. From the fit to theexperimental data we obtained J_(BR)=αρL)β, where α=1.3×10⁻⁶ and β=0.73.For graphene-on-SCD, the slope is β=0.51. Previously, the scaling with(ρL)^(−β) (where β=0.6-0.7) was observed in carbon nanofibers (CNF),which had a similar aspect ratio. Such J_(BR)(ρL) dependence wasexplained from the solution of the heat diffusion equation, whichincluded thermal coupling to the substrate. However, the thermallyinduced J_(BR) for CNF was ˜10⁶ A/cm²—much smaller than the recordJ_(BR)≈1.8×10⁹ A/cm² we obtained for graphene-on-SCD.

In a preferred embodiment, the UNCD thin films were grown on 100-mmdiameter Si substrates 165 in the 915 MHz large-area microwave plasmachemical vapor deposition (“MPCVD” hereinafter) system 175 (DiamoTek1800 series 915 MHz, 10 KW from Lambda Technologies Inc.) operating inthe clean room at the Argonne National Laboratory. Prior to the growth,silicon substrate were deposited with 10 nm tungsten layer using sputterdeposition process followed by nanodiamond seeding treatment using thenanodiamond suspension containing dimethylsulphoxide (DMSO) solution(ITC, Raleigh, N.C.). Details about MPCVD and seeding process for theUNCD growth are described in Example I. The single crystal diamonds usedfor this study were type IIb with (100) orientation (Delaware DiamondKnives) polished from both sides down to ˜3-nm RMS roughness. Apre-cleaning procedure using acid wash and solvent cleaning was used toetch any contaminants from the surface. The H-termination process withmicrowave plasma was carried at the substrate T=700° C. using H₂ flow of50 sccm and chamber pressure of 30 mbar for 10-15 mins. The processeliminates any hydrocarbon and oxygenated impurities and produces cleanterminated diamond surface. We defined the top-gate region using EBL(NPGS controlled Leo 1550) and performed ALD (Cambridge Nanotech) of20-nm thick Hf0 ₂ at T=110° C. The lift-off of ALD was done in hotacetone (T=60° C.) for ˜2 hours. We often observed oxide leftovers atthe edges of the defined 9 regions, which can lead to discontinuities inthe following metal layer. To avoid this problem, we designed HfO₂-layerinsert under the entire region of gate electrode and pad. We then usedEBL to define the source, drain and top gate electrodes regions anddeposit Ti/Au (10 nm/100 nm) by E-beam evaporator (TemescalBJD-1800).The gate leakage in our devices was very low (much smallerthan 0.1 nA/μm₂). We established that our polished UNCD/Si substrates donot require a seeding layer for ALD of HfO₂ gate dielectric.

In yet another embodiment, the graphene 110 can be grown at lowtemperatures (about 400-500° C.). Preferably this process involvesgraphene growth directly on an Ni surface 250 on a substrate (like thediamond substrate 100) using a solid carbon precursor which allowsgraphene growth of single or multiple layers in a highly controlledmanner. Such a method is quite compatible with complementary metal oxidesemiconductor (“MOS” hereinafter) manufacturing processes.

In this preferred embodiment illustrated schematically in FIGS. 13A-13C,several steps are used to produce the desired graphene layers. Thesubstrate is preferably Ni which can take the form of Ni thin film (suchas, for example, 300 nm) or even bulk Ni foil. In the case of thin filmNi as the substrate, the Ni thin film 250 is deposited on the siliconsubstrate 165 with the intermediate titanium (Ti) adhesion layer 200(thickness: 10-20 nm) (see FIG. 13A). In other embodiments othercatalytically suitable, like-performing transition metal or transitionmetal alloys substrates can be used to support the polymer layer 280deposited thereon for processing. Further, the base substrate need notbe a Si substrate 165, but can be any compatible substrate known in theart. In addition other conventional adhesion layers 200 can be usedbesides Ti which are compatible with the transition metal layer 250. Theuse of a silicon dioxide (SiO₂) layer 270 is not required but could beused in case of device isolation. The next step in the process in FIG.13B is to mix two polymers 280 in the solid form (n-octacosane andn-tetracosane) in 1:1 (wt. percentage) and heat the mixture on a hotplate to a temperature of about 80° C. so that it converts into aviscous liquid form. It is also important to note that these polymershave a relatively low melting point (less than about 80° C.) and highvapor pressure. Therefore, they decompose at very low temperatures whichis essential for the low temperature growth of graphene. Also in thepreferred embodiment only the combination of both of these polymers inthe previously mentioned (in wt %) concentration works to facilitate thegrowth of graphene on Ni at low temperatures. Use of only one of thesepolymers will not work. Therefore it is important to note that otherpolymers containing a similar mixture of saturated aliphatic hydrocarbonand alkane hydrocarbon with low melting point will also work for ourprocess.

The prepared polymer solution is then spin-coated on the surface of theNi film 250 followed by cooling the substrate 165 to room temperature sothat the polymer solution converts into a thick solid layer. The polymercoated Ni substrate 250 is then transferred into the vacuum furnace forgraphene growth. The Ar gas (2000 sccm) was then flown into the chamberwith the chamber pressure maintained at 300 Torr. The temperature of thevacuum furnace was then raised at around 400-500° C. and maintained for15-20 mins. This process essentially discomposes the polymer layer onthe top of the surface of the Ni 250 and starts precipitating a carbonrich layer on the Ni surface 250. In the next step shown in FIG. 13C,the substrate 165 is cooled from 400-500° C. to room temperature at therate of about 15-30° C./min. This rapid cooling rate converts thegraphitic carbon into the graphene layers 110. The yield and quality ofthe graphene layers 110 can be improved further by using carbonprecursor gas to accelerate the growth of graphene 110. In that case, anAr/Ethanol gas mixture can be flowed into a chamber during the growth at400-500° C. for few minutes to grow large grain size of the graphene110.

In FIGS. 14A and 14B are shown the Raman spectra of the graphene 110grown at 400° C. and corresponding optical micrograph of the Ni surface250 respectively, confirming the graphene growth. FIGS. 14C and 14D showthe Raman spectra of the graphene 110 grown at 500° C. and correspondingoptical micrograph of the Ni surface 250 respectively. The graphenequality is better at higher temperature as expected.

This method therefore allows growing multilayer graphene 110 on Nisubstrate 250 at low temperature (about 400-500° C.). This method alsoallows growth of graphene 110 at temperatures compatible with a typicalCMOS thermal budget, which opens-up the possibility of integration ofthe graphene 110 with CMOS electronics. This is a crucial step indeveloping graphene based hybrid devices with efficient thermalmanagement. No source of carbon containing gas for the graphene growthis required since a polymer layer coated on the substrate itself acts asa solid carbon source. The low temperature process requires less energythan the conventional growth process that occurs at 1000° C., whichdirectly affects economics of fabricating graphene devices on commercialscale. The low temperature growth process was done on a 4 inch diameterwafer but could be easily scalable to large area.

METHODS

The near edge ray absorption fine structure spectroscopy (NEXAFS) of theUNCD sample was carried out at the University of Wisconsin SynchrotronRadiation Center Facility. The data was acquired at HERMON beam atcarbon K edge with high energy resolution (0.2-0.4 eV). The spectra weretaken in the total electron yield (TEY) mode with the incident photonbeam normal to the sample. Special care was taken to correct for thecarbon contamination from the X-ray beam optics and transmissionstructure from the monochromator. Details of the measurements aredescribed in the Examples.

In the embodiment of direct growth of graphene on a diamond substrate,as shown in FIG. 6 the starting material is either single crystaldiamond 100 or UNCD/NCD thin film 100 deposited on a silicon substrate260 (shown in phantom) with Ni thin film (typical thickness: 30 nm) 250deposited on the top of the diamond 100 or the UNCD/NCD thin film 100.The next step in the process is to anneal the substrate in vacuumfurnace in H₂/Ar gas mixture (50:50 ratio) at around 800-1000° C., for15-20 mins. In one embodiment, the substrate is heated to the annealingtemperature in about 30s for annealing. This process essentiallydissolves the Ni 250 into the diamond 100 due to the strong catalyticreaction with the diamond 100. During this process, part of the Ni 250diffuses into the diamond 100 and starts graphitizing the diamond 100.At the end of this process, a few nanometers of the diamond surface fromthe top surface is completely graphitized; and the layer mostly consistsof graphitic carbon. The next step, involves cooling the substrate from800-1000° C. to room temperature with the rate of about 30° C./min atthe beginning to about 15° C. at the end. In one embodiment, the coolingis performed at a rate of about 600° C./minute. This rapid cooling rateconverts the graphitic carbon into the graphene layers 110. The yieldand quality of the graphene layers 110 could be improved further byusing a carbon precursor gas to accelerate the growth of the graphene110. In that case, we used As/Ethanol gas mixture at 1000° C. for fewminutes to grow large grain size graphene 110. It is preferable that theNi content should be small enough so that it ends up utilizing all ofthe Ni during the growth; and therefore the high quality growth of thegraphene 110 can be achieved without trace amount of Ni in sub-surfaceregions of the diamond 100.

In one embodiment, a rather than a normal high temperature vacuum oventechnique, a Rapid Thermal Annealing “RTA” is utilized. Animplementation of such is illustrated below in Example III. This issignificant development over existing methods which mostly producepolycrystalline graphene and requires 4-5 hours in total for a singlegraphene growth run. Additionally, it has been shown that the RTPprocess can produce graphene on wafer-scale (4″ wafer) and can beextended to even large area. With increased interest in two-dimensionalcarbon material, graphene, the challenges in growing the large scalehigh quality films become a main hurdle for using it in differentapplications, such as coatings, bio sensors, microelectronics,photonics, etc. Most of the existing methods have certain limitations.Mechanical exfoliation, commonly used in research, is not suitable forlarge areas. Molecular assembly, used for nanoelectronics, is costly andcommercially not viable. Liquid-phase exfoliation results in impuritiesand discontinuity of the films, which is not suitable for devicefabrication. Chemical vapor deposition (CVD) process requires additionaltransfer process. Existing methods of graphene growth on SiC are costlyand require high temperature. Diamond offers several unique propertiessuch as low trap density for charges, chemically inert, and high thermalconductivity. Moreover, diamond by itself showed a lot of usefulapplications in MEMS and in bio-medical sensors.

One embodiment relates to a process based on rapid thermal annealing ofdiamond film in the presence of metal catalyst is promising as comparedto other existing methods of growing graphene without the transferprocess. The MD simulation results discussed below indicate newmechanism of graphene nucleation through initiation of graphenenucleation on Ni(111) and enhanced graphene growth through continuoussupply of carbon from the amorphized diamond underneath. No Nickeletching step is required since it diffuses very fast through UNCD grainboundaries and segregates at the UNCD/Si interface. The scheme offabricating suspended graphene membranes on diamond offers uniqueopportunity to take full advantages of intrinsic properties of graphene,for the first time. The graphene-on-diamond platform is promising forthe development of high performance nanoelectronic devices.

FIG. 31 illustrates Fabrication of top-gate graphene FET on diamond. Thetop gate graphene FETs on UNCD with good charge carrier mobility of˜2000 cm²V⁻¹s⁻¹ for electrons and carrier density of ˜3.5×10¹² cm⁻²ismeasured at RT.

FIG. 32 illustrates a possible mechanism for the graphene growth ondiamond. It should be further appreciated that nanopatterning can bepossible using patterned nickel on UNCD.

In one embodiment, the graphene is formed in less than a minute uponcooling. In a further embodiment, the graphene is formed between 1nanosecond and one minute.

Example I

Fabrication of the graphene devices 170 relies on the fact that thegraphene 110 can be visualized using optical microscopy if prepared ontop of UNCD/Si wafers with a certain thickness of the UNCD 100. Beforethe diamond growth and graphene device fabrication we estimated anapproximate thickness of UNCD required to make graphene visible usingFresnel's law. The results were checked experimentally. Consider thecase of normal light incidence from air (refractive index n_(o=)1) on atri-layer structure consisting of the graphene 110, the diamond 100, andthe Si 165 as shown in FIG. 8. The visibility of the graphene 110 ondifferent types of substrates originates from both the relative phaseshift and amplitude modification induced by the graphene layer 110. Thecomplex refractive indices of silicon and diamond used in thecalculations were adopted from literature The Si substrate wasconsidered semi-infinite and the refractive indices of Si, n₃, wereassumed to be wavelength dependent. The refractive index of graphene isassumed to be independent of λ: n_(g)(λ)=2.6−1.3i

Calculations of the contrast spectra were performed using conventionalmethods:

$C = \frac{{R_{{without}_{—}{graphene}}(\lambda)} - {R_{{With}_{—}{graphene}}(\lambda)}}{R_{{Without}\text{-}{graphene}}(\lambda)}$

Here R_(without) _(_) _(graphene)(λ) is the reflection spectrum from thediamond substrate and R_(with) _(_) _(graphene)(λ) is the reflectionspectrum from the graphene sheet.

$\begin{matrix}{{R(\lambda)} = \left| \frac{r_{a}}{r_{b}} \right|^{2}} & (1) \\{r_{a} = \left( {{r_{1}e^{i{({\beta_{1} + \beta_{2}})}}} + {r_{2}e^{- {i{({\beta_{1} + \beta_{2}})}}}} + {r_{3}e^{- {i{({\beta_{1} + \beta_{2}})}}}} + {r_{1}r_{2}r_{3}e^{- {i{({\beta_{1} + \beta_{2}})}}}}} \right)} & (2) \\{r_{b} = \left( {e^{i{({\beta_{21} + \beta_{2}})}} + {r_{1}r_{2}e^{- {i{({\beta_{1} + \beta_{2}})}}}} + {r_{1}r_{3}e^{- {i{({\beta_{1} + \beta_{2}})}}}} + {r_{2}r_{3}e^{- {i{({\beta_{1} + \beta_{2}})}}}}} \right)} & (3)\end{matrix}$where r₁=(n₀−n₁)/(n₀+n₁), r₂=(n₁−n₂)/(n₁+n₂) and r₃=(n₂−n₃)/(n₂+n₃) arethe reflection coefficients for different interfaces and β₁=2πn₁(d₁/λ),β₂₌2πn₂(d₂/λ), are the phase differences when light passes through themedia, which are determined by the path difference of the twoneighboring interfering light beams.

The simulations were carried out using conventional MATLAB software. Theincident wave was assumed to be perpendicular to the plane of themultiple layers. This is a reasonable assumption because the totalthickness of graphene/diamond is much smaller than the depth of focus ofthe objective lens used in most experiments (0.9-1.8 μm for λ=0.4-0.8 μmand the numerical aperture of 0.95) within the depth of focus. For thisreason the wave front of the focused light is almost flat. FIG. 9 showsthe calculated grayscale plot for the expected contrast as a function ofthe diamond thickness and wavelength with the diamond thickness rangingfrom 0 to 800 nm and the wavelength ranging from 400 nm to 700 nm. Onecan see from FIG. 9 that graphene on diamond/Si exhibits a negativecontrast, i.e., graphene on diamond/Si appears brighter than thesubstrate. Fixing the wavelength at 555 nm (the most sensitivewavelength to human eye) one gets the thickness of UNCD with the highestcontrast to be around 650 nm (see FIG. 10).

Example II

The effective thermal conductivity of the polished UNCD/Si wafers wasmeasured using the transient plane source (TPS) “hot disk” techniquewhich is conventional and well known. The thermal conductivity of SCDwas measured with the “laser flash” technique, which is more accuratefor the materials with high K values. The measured thermal conductivitydata was used to determine the thermal resistance of the substrates.

In the TPS method, an electrically insulated flat nickel sensor isplaced between two pieces of the substrate. The sensor is working as theheater and thermometer simultaneously. A current pulse is passed throughthe sensor during the measurement to generate the heat wave. Thermalproperties of the material are determined by recording temperature riseas a function of time using the equation, ΔT(τ)=P(π^(3/2)rK)⁻¹D(τ),where τ=(t_(m)α/r²)^(1/2), α, is the thermal diffusivity, t_(m) is thetransient measurement time, r is the radius of the sensor, p is theinput heating power, and D(τ) is the modified Bessel function. The timeand the input power are chosen so that the heat flow is within thesample boundaries and the temperature rise of the sensor is notinfluenced by the outer boundaries of the sample. To make sure that oursystem is properly calibrated we measured thermal conductivity ofstandard Si wafers and compared the results with the literature values.One can see FIG. 11 that our measured data are in excellent agreementwith the previously reported values. The temperature dependence of thethermal conductivity K˜1/T is also in agreement with the theory forhigh-quality crystals. FIG. 12 presents the measured K_(eff)(T) for areference Si wafer and a UNCD/Si composite substrates. The Si wafer's Kscales as ˜1/T, which is expected for semiconductor crystals near andabove room temperature. The effective thermal conductivity of theUNCD/Si becomes larger than that of Si at higher temperature due toimproved inter-grain phonon transparency in UNCD.

Example III Metal Induced Transformation of Diamond Into Single DomainGrapehene on Wafer Scale in Seconds

The presently described example reports a new process of graphenesynthesis, based on rapid thermal annealing of diamond film in thepresence of metal catalyst, which outperforms all other existing methodsof growing graphene without the transfer process and enables singledomain growth of graphene. In this context, single domain graphene, orsingle crystal graphene, refers to a graphene with a continuousarrangement of hexagonally bonded carbons. Any non-hexagonal bonding,multilayer, or gaps would “break” the structure and define the boundaryof the crystal.

Because of the grain boundaries in the diamond film nickel segregatesthrough the UNCD during rapid thermal annealing process. This factbenefits in graphene growth directly on the diamond surface, allowing toproduce the wafer scale diamond films covered with graphene. The qualityof the produced graphene films was checked with Raman analysis atdifferent points of the wafer as well as with XPS analysis demonstratingthe clear carbon signature without any presence of nickel on the surfaceafter the annealing process (FIG. 15), thus confirming complete nickelsegregation inside the UNCD layer. Also, detailed analysis of carbonpeak demonstrates presence of only sp² bonded carbon on the surface,thus indicating high purity, without any modification (such asoxidation), nature of graphene.

More detailed surface analysis of the produced wafer indicates growth ofcontinuous graphene film. FIG. 16A demonstrates the quality of theas-grown film, indicating smooth surface structure with occasional foldsof graphene layer occurring. Some of the folds seen on the atomic forcemicroscopy (AFM) image are responsible for the defect peak in Ramansignature. The presence of the folds is assumed to be due to UNCDroughness and the annealing speed.

To be able to vary the thickness of the grown graphene film thetemperature of the process was varied from 800° C. up to 1000° C. (FIG.16B). Due to substrate effect of underlying diamond film the grapheneRaman signature shows presence of defect peak D (at ˜1335 cm⁻¹) and lowintensity ratio 2D (at ˜2650 cm⁻¹) to G (at ˜1585 cm⁻¹) bands incomparison to that of single layer graphene (2:1), grown on copper foil(FIG. 16B). Moreover, significant blueshifts of G and 2D bands as wellas increase 2D-band full width half maximum (fwhm) for graphene ondiamond are seen. This effect occurs due to interfacial covalentlybonded to UNCD carbon layer with graphene like lattice, which changesthe lattice constant and electronic properties of top graphene layer.Similar effect was seen before for graphene grown on SiC substrate. Incase of low 800° C. annealing temperature the number of graphene layersis significantly reduced, though as-grown graphene contains more folds,while in case of annealing temperature increase the thicker graphenefilm with smoother structure is observed. Therefore, the thickness ofgrown graphene can be tuned by varying temperature and time ofannealing. The quality of the grown graphene on UNCD film was alsoevaluated by measuring the sheet resistance of the grown film using thefour point probe method. The sheet resistance of received graphene/UNCDfilms varies from 0.09 ohm/square for thick graphene sample grown at1000° C. up to 3.1 ohm/square for single layer graphene grown at 800° C.

In addition to growing high quality planar sheets of graphene directlyon the UNCD surface, free standing graphene films were grown over theholes made in diamond (FIG. 17). FIG. 17A demonstrates that annealing ofthe Ni/UNCD sample resulted in 3 holes being completely covered withgraphene with 1 hole remaining partially covered with graphene.

To determine the quality of the grown graphene it was transferred to thetransmission electron microscopy (TEM) grid and the selected areaelectron diffraction (SAED) pattern was identified to demonstrate thesingle crystal growth (FIGS. 17D and 17E).

Detailed Raman study of the graphene on the hole indicates lowering theintensity of defect peak and increasing the intensity of 2D peak, thoughthe signature does not correspond yet to the single layer graphene dueto shallow shape and small size of the hole (FIG. 18).

To explore the possible mechanism of the direct graphene/diamond growth,two types of molecular dynamic (MD) simulations were performed. FIG. 19demonstrates the schematic of the graphene growth procedure on diamondsubstrate. Based on the received experimental and theoretical results,it is believed that the new mechanism of graphene nucleation and growththrough Ni induced transformation of diamond into the graphene istwo-fold: 1) Carbon diffusion through the nickel film with eventualsegregation of nickel down through the diamond grain boundaries (FIG.19E); 2) nucleation of graphene islands on Ni (111) with lateral growthof graphene film until full coverage is achieved (FIG. 19F).

When the system is heated to elevated temperatures, nickel atoms startto segregate down through the diamond grain boundaries while carbonatoms separate from the diamond lattices by forming amorphous carbon ontop of nickel (111) film. As it was demonstrated by Hofmann et al.surface diffusion of carbon has low barrier on the Ni (111) surface,with results in fast rate of following graphene formation. Meanwhile, Ni(111) plays the role of a template to facilitate nucleation of hexagonalstructure from amorphous carbon layer, and when graphene layerseventually meet they form mostly uniform and defect-free coverage.Preferential Ni (111) crystal plane of the sputtered nickel films wasconfirmed experimentally by x-ray diffraction (XRD) analysis.

The described procedure of growing high quality wafer-scale graphenefilm directly on insulating substrate via rapid thermal annealing ofdiamond film in the presence of metal catalyst, outperforms all otherexisting methods of growing graphene without the transfer process.Tuning of graphene thickness is achieved through the annealingtemperature variation, indicating, that at lower 800° C. temperature thereceived graphene film consists only from few layers, while increase intemperature up to 1000° C. results in multi-layer graphene. Themolecular dynamic (MD) simulation results indicate new mechanism ofgraphene nucleation and growth through Ni induced amorphization ofdiamond. The novel scheme of fabricating suspended graphene membranesdirectly on diamond offers unique opportunity to take full advantages ofintrinsic properties of graphene, for the first time. Thus, thegraphene-on-diamond platform is promising for the development of highperformance, energy efficient nanoelectronic devices.

Methods

50nm of Nickel have been deposited on the ultra nano-crystalline diamond(UNCD) surface by e-beam sputtering deposition. After this, the sampleswere processed in a rapid thermal annealing system under 800-1000° C.temperature for 60 seconds while flowing 500 sccm of the forming gasmixture (5% of H₂ and 95% of N₂). This procedure resulted in growing theuniform layer of graphene directly on the UNCD surface.

Fabrication Procedure

Ultrananocrystalline diamond (UNCD) film is grown by a microwaveplasma-enhanced CVD (MPCVD) process using an Ar-rich/CH₄ chemistry (Ar(99%)/CH₄ (1%)) on silicon substrate. The thickness of UNCD films variedfrom 200 nm up to 300 nm.

50 nm of Nickel have been deposited on the UNCD surface by e-beamsputtering deposition. After this, the samples were processed in a rapidthermal annealing system under 800-1000° C. temperature for 60 secondswhile flowing 500 sccm of the forming gas mixture (5% of H₂ and 95% ofN₂). The typical recipe for the annealing process at 1000° C. isdemonstrated at FIG. 20. This procedure was showing to be effective forgrowing the uniform graphene layers on the UNCD surface. FIG. 21 showsthe schematic of deposited layers before and after the annealing processas well as the cross-section images of the films.

Single-Layer Graphene Characterization

To evaluate the quality and thickness of the grown at 800° C. graphenelayer, it was transferred onto silicon dioxide (SiO₂) substrate usingthermal release tape procedure. Due to the strong adhesion to theunderlying diamond substrate, it was possible to receive the transferredgraphene in form of flakes. FIG. 22 presents AFM image of the receivedsingle layer graphene flakes.

Free-Standing Graphene

For free-standing graphene growth process the procedure was asfollowing: 1) 500 nm deep holes of diameter varying from 300 nm up to 1μm are made in 50 nmNi/UNCD film using SEM ion beam milling; 2) RTPannealing steps are performed following the same procedure as mentionedabove for the plain UNCD sample (FIG. 23).

Nickel Patterning for Selective Graphene Growth

Patterning of the nickel layer was performed by depositing 50 nm ofnickel through a shadow mask. After RTP processing, the resulting filmdemonstrated selective growth of graphene on diamond at the places wherenickel film was deposited (FIG. 24).

Characterization

X-ray photoemission spectroscopy (XPS) analysis was performed by ahome-built X-ray photoelectron spectrometer, which includes ahemispherical electron energy analyzer of 0.9eV energy resolution and anon-monochromated Mg K-alpha soft x-ray source source at 1253 eV.

Raman spectroscopy analysis has been performed by an Invia ConfocalRaman Microscope using the red laser light (λ=633 nm) to confirm theformation of a graphene layer on the UNCD surface. Intensity andposition of the characteristic G and 2D graphene peaks, as well as thefull width at half maximum (fwhm) of 2D peak in the Raman spectra showvariation in the number of graphene layers grown at differenttemperature. The presence of defect peak D can be explained by graphenefolds clearly seen in SEM and AFM images. Also the roughness of theunderlying UNCD grains affects the overall quality of the growngraphene.

Scanning Electron Microscopy (SEM) images were received using FEI Nova600 Nanolab dual-beam microscope with focused ion beam (FIB) used formaking the cross-section of the grown layers. Deposition of two platinumfilms on the surface before making the cross-section is performed toprotect the sample. Energy-dispersive X-ray spectroscopy (EDS) analysisof the layers confirmed the position of nickel layer (as shown on thefigure) before and after annealing, and carbon layer, confirming nickelsegregation inside the UNCD and thus producing direct graphenedeposition on the diamond surface.

Atomic force microscopy (AFM) measurements were performed to demonstrate3D structure of the grown layers. For this purpose, the images wereacquired by an AFM Veeco Microscope in ambient air conditions (RH˜40%)using a n-doped silicon tip in tapping mode.

Transmission electron microscopy (TEM) studies were performed on twodifferent types of samples: grown graphene layer and the cross sectionof graphene grown on UNCD. In the first case, the sample was prepared byusing thermal release tape to transfer the top layer on the TEM 300 meshcopper grid. In the second case, the sample was prepared using focusedion beam at the SEM instrument, when the sample was cut at the crosssection and then attached to the TEM lift-out grid using FIB milling.Observation of the single crystal graphene is performed usingtransmission electron microscope (TEM) JEOL JEM-2100F.

X-ray Diffraction (XRD) analysis was performed with Bruker D2 PhaserDiffractometer to demonstrate the crystal orientation of the grownNickel films on UNCD wafer.

Molecular Dynamic Simulations

Generation of diamond grain boundary: Reactive molecular dynamics (MD)simulations with dynamic charge transfer between atoms is used toinvestigate the nucleation and growth kinetics as well as the earlystages of nanoscale graphene growth in a system comprising of Ni(100)surface placed on top of a diamond grain-boundary. The simulations of atypical grain boundary in a ultrananocrystalline diamond (UNCD) weredone on the Σ13 twist (100) grain boundary (GB). It was reportedpreviously that this particular grain boundary presents a goodcompromise between the computational requirements and the need of areasonably large cell size needed to reproduce a general high-angle GB.The procedure for the generation of the grain boundary is as follows: Asa first step, a relative rotation is performed of the two halves of thecrystal by 67.4° about the z axis that is normal to the common (100)plane. Such a rotation gives a coincident site lattice periodic in twodimensions with a planar cell containing 13 atoms per (100) plane. Athree- dimensional periodic model of the crystal was constructed withplanar repeating grain boundaries. Note that the periodicity in thethird dimension is achieved by extending the two grain boundaries perrepeating cell. Each cell has a thickness of 16 layers and thus contains208 carbon atoms. This generated grain boundary was subjected to arelaxation or an equilibration procedure. During the initial relaxation,the dimensions of the cell in the GB plane were fixed because of therigidity of the diamond lattice. However, the simulations do allow forexpansion in the z direction to reproduce the volume increase in thegrain boundary region. Subsequently, thermal equilibration of thisinitial structure was performed by simulating at a high temperature of1500 K for 100 ps. Simulated annealing was used to gradually lower thetemperature, and the final structure was optimized by a conjugategradient method. The initial equilibrated grain boundary structure isshown in FIG. 25.

Potential Model for Reactive Simulations: To simulate the growth ofgraphene on diamond surfaces and grain boundary, molecular dynamic (MD)simulations were utilized employing a reactive force-field (ReaxFF)potential model that allows for variable and dynamic charge transferbetween atoms. In particular, reactive force-field (ReaxFF) implementsthe feature of quantum chemistry calculations, including molecularassociation/dissociation and charge transfer between cations and anions,and therefore ensure a more accurate description of the oxidationsimulation. By calculating many-body interactions of a single particle,characteristics of quantum chemistry effect are employed inmultiple-components of particle interactions as shown in Eq. (4), suchas bond energy, over/under coordination, lone-pair energy, valenceangle, torsion, hydrogen bond, van der Waals, and Coulomb.E _(total) =E _(bond) +E _(over) +E _(under) +E _(lp) +E _(val) +E_(tors) +E _(H) +E _(vdw) +E _(Coul)  (4)Additionally, the temporal charges of cations/anions are calculatedusing the electronegativity equalization method as shown in Eq. (5).

$\begin{matrix}{{E(q)} = {\sum\limits_{i}\left\lfloor {{\chi_{i}q_{i}} + {\eta_{i}q_{i}^{2}} + {{{Tap}\left( r_{ij} \right)}k_{c}\frac{q_{i}q_{j}}{\left( {r_{ij}^{2} + \gamma_{ij}^{- 3}} \right)^{1\text{/}3}}}} \right\rfloor}} & (5)\end{matrix}$

In the above equation, q, χ, η, Tap(r), γ, and k_(C) are ion charge,electronegativity, atomic hardness, 7th order taper function, shieldingparameter, and dielectric constant, respectively. Detailedimplementation and development of ReaxFF models for Ni—C interactionscan be found in the work by Adri et al. It is capable of treating bothmetallic and ceramic systems as well as bond formation and bond breakageinvolved in the graphene nucleation and growth processes. Additionally,it can take into account the presence of multiple coordination as wellas valence states in the growing graphene film. The simulation set-up(FIG. 25) and computational details are summarized below.

Simulation details: The dynamical evolution of graphene formationinvolves several steps which includes diffusion of Ni atoms through thediamond grain boundary, reactive amorphization of the adjacent carbonatoms and Ni catalyzed graphitization. These events are captured usingthe ReaxFF potential model. A schematic showing the actual simulationset-up is shown in FIG. 26. The simulation cell comprised of Ni thinfilm: placed on top of the Σ13 twist (100) GB. Prior to the actualsimulations of graphene nucleation and growth, the system comprising ofNi on top of grain boundary are subjected to an equilibration procedureat 300 K. About 100000 MD steps using isokinetic MD was performed. Thetemperature was maintained constant at using a Nose-Hoover thermostat.Both the Ni thin film and the diamond surfaces forming the grainboundary are allowed to freely relax during these equilibration runswith no charge transfer. The equilibrated samples are then simulated ina NVT ensemble for 1 ps with dynamic charge transfer using the ReaxFFpotential model to generate the final 300 K relaxed configuration.

The slab of Ni (100) is then placed on top of the diamond surfaces; thegrain boundary is normal to the Ni(100) surface (FIG. 26). Thesimulations of Ni-induced amorphization of carbon and subsequentgraphization are all carried out at high temperature of ˜1200 K. Tofacilitate comparisons with the experiments, the graphene growthsimulations were performed in both hydrogen and hydrogen-freeenvironments. The hydrogen atmosphere was created by introducing H₂molecules in the simulation box with their x, y, and z positions chosenrandomly. In the case of simulations in the hydrogen environment,reflecting boundary conditions are imposed in the z-direction to confinethe molecules that might reach the simulation box limit. The gaspressure is thus maintained constant during these simulations.

In all the simulations, the atomic velocities are chosen from aMaxwell-Boltzmann distribution corresponding to the requiredtemperature. The equations of motion are integrated using a leapfrogscheme with time steps of ifs. The charge relaxation procedure used tominimize the electrostatic energy subject to the electro-neutralityprinciple is very time consuming. Hence, the atomic charges were updatedevery 10^(th) MD step. The influence of a more frequent charge updatewas found to have no influence on the observed simulation results. Thesimulations were carried out using the Large-scale Atomic/MolecularMassively Parallel Simulator (LAMPPS).

Nickel Film Properties

XRD analysis of grown 50 nm Ni films was performed to explore theimportance of crystal orientation for the uniformity of graphene layers.FIG. 22 demonstrates that nickel films used for successful graphenegrowth have preferential orientation of Ni (111).

To understand the impact of the surface orientation of underlying Nisubstrate on graphene growth, molecular dynamics (MD) simulations wereperformed of annealing amorphous carbon deposited on Ni substrates withsurface normal oriented along the crystallographic 111 and 001 planes.The interactions between Ni and C atoms were modeled by a reactive forcefield (ReaxFF) with parameters obtained from Mueller, J. E., van Duin,A. C. T. & Goddard, W. A. Development and Validation of ReaxFF ReactiveForce Field for Hydrocarbon Chemistry Catalyzed by Nickel. The Journalof Physical Chemistry C 114, 4939-4949, doi:10.1021/jp9035056 (2010).For each of these simulations, an initial configuration (t=0) wasgenerated by placing a layer of completely disordered (amorphous) carbon(with nearest C-C spacing ˜2-2.5 Å) on Ni substrate ˜40 Å×40 Å×50 Å withdesired surface orientation, as shown in FIGS. 22a and 22e . Periodicboundary conditions were implemented in the plane of the surface. Thetemperature of the system was ramped from 300 K to 1600 K over 50 ps ina canonical ensemble (NVT) with Nose-Hoover thermostat, as implementedin LAMMPS; subsequently, the temperature was held at 1600 K for anadditional 150 ps.

Direct visualization of the MD trajectories showed that in the initial˜5 ps, when the temperature is ˜300 K, the density of amorphous carbontends to increase, along with ordering of C atoms and formation of C-Cbonds (FIGS. 28B and 28F). As indicated by FIGS. 28B and 28F, thenucleation of graphene islands i.e., with 6-membered carbon rings occurson all Ni surfaces; however, the Ni (111) exhibits much highernucleation of graphene like C-rings as compared to Ni(001) surface. Toprovide a quantitative assessment of this orientation preference, therate of formation of C-rings containing 5--8 C members on Ni substratesof different orientations in the initial ˜5 ps was calculated. Fromthese calculations, among the low-index surfaces of Ni, it was foundthat the C rings form at the highest rate on Ni (111) ˜30 rings /ps;this rate is more than twice as fast as that on Ni (001) surface (˜12rings/ps). Interestingly, most of the rings (˜65%) that form on Ni (111)surface are 6-membered (like the hexagons in graphene), while thepopulation of 6-membered rings nucleated on Ni (001) surface is fairlylimited, which is ˜25% of the total nucleated C-rings [FIG. 28F]. Thisclearly indicates that graphene formation is most favorable on Ni (111)among the low-index planes.

After this initial time period, the C atoms continue to re-arrange toreduce the number of defects (i.e., off 6-membered rings, holes) but nonew C-rings nucleate. As shown in FIG. 28C, the monolayer graphene thatforms on Ni (111) surface features the least number of defects, andcovers nearly the entire substrate. On the other hand, on Ni (001),graphene forms as patches and is highly defective [FIG. 28G]. Theresults were observed to be robust; the effect of Ni surface orientationon graphene growth is unaffected by the temperature schedule and thehighest temperature achieved during the annealing. The kinetics ofre-organization of C-atoms to reduce the defects, as expected, is slowat lower temperatures.

Upon close inspection of the atomic structure of Ni surfaces alongdifferent orientations, one plausible explanation for preferentialnucleation of 6-membered C rings on Ni (111) as opposed to Ni (001)surfaces. The Ni atoms on (111) plane are arranged on a close-packedtriangular lattice (FIG. 28D), which closely resembles the honeycombstructure of graphene; this enables Ni (111) substrate to provide asuitable template for the formation of nuclei for graphene growth, i.e.,6-membered C-rings. Ni (001) plane, on the other hand, exhibitrectangular lattice (FIG. 28H) and cannot provide such a template.Furthermore, recent first-principle calculations have reported that thediffusion of C on Ni (111) surface is much lower than that on Ni (001)(˜0.5 eV on Ni (111); ˜1.9 eV on Ni (001)). This leads to substantiallyhigher diffusion of C on Ni (111) plane, which explains the faster rateof graphene growth on Ni (111).

Graphene on Diamond Based Transistors.

In order to test the electron mobility of the CVD grown graphene on UNCDsubstrate a number of graphene top-gate field-effect transistors(TG-FETs) was fabricated. The top-gate dielectric layer which consistsof 20-nm-thick HfO₂ was grown by the atomic layer deposition (ALD). Theelectron beam lithography (EBL) technique was used to define the source,drain and gate electrodes. The films of Ti/Au with the thickness of10-nm/100-nm were deposited by the electron beam deposition to form themetal contact to the devices. FIG. 29 shows an optical microscope imageof a typical fabricated device. The scale bar is 100 μm. The dark partis a dielectric layer of HfO₂ with the size of 200 μm by 300 μm. Thegate electrode is 200 μm in width and 120 μm in length. The source anddrain electrodes are 200 μm in width and 50 μm in length.

The current-voltage (I-V) characteristics of the top-gated devices weremeasured using a semiconductor parameter analyzer (see FIG. 29). First,the source-drain current versus source-drain voltage was measured atzero gate bias via two terminal measurements. The linearity of I_(ds) vsV_(ds) curve confirms the high-quality Ohmic contact. FIG. 29b presentssource-drain current as a function of the gate bias. The source-drainvoltage was kept at 0.1 V during this measurement while the gate biasswept from −2 V to 5 V. The V-shape I_(ds)-V_(gs) curve ischaracteristic for graphene and indicates that the charge carrier typecan be switched from electrons to holes by tuning the gate bias. TheDirac point of the tested device is around −1 V. The carrier mobility ofelectrons and holes can be extracted using the Drude formula (Eq. 6):

$\begin{matrix}{\mu_{FE} = {\frac{g_{m}}{C_{g}V_{ds}}\frac{L_{g}}{W}}} & (6)\end{matrix}$where

$g_{m} = \frac{{dI}_{ds}}{{dV}_{g}}$is the transconductance,

$C_{g} = \frac{ɛ_{r}ɛ_{0}}{d}$is the gate capacitance per area and relative permittivity of HfO₂ is25. L_(g) and W are the length and width of the gate, respectively. Thehighest electron mobility extracted for the tested device was around2000 cm²/Vs.

The foregoing description of embodiments of the present invention hasbeen presented for purposes of illustration and description. It is notintended to be exhaustive or to limit the present invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of thepresent invention. The embodiments were chosen and described in order toexplain the principles of the present invention and its practicalapplication to enable one skilled in the art to utilize the presentinvention in various embodiments, and with various modifications, as aresuited to the particular use contemplated.

The invention claimed is:
 1. A method of forming single domain grapheneon a substrate, comprising the steps of, providing a diamond substrate;forming a transition metal layer on the diamond substrate; forming atleast one hole in the transition metal layer and diamond substrate;dissolving the transition metal layer into the diamond substrate by anannealing step; and cooling the substrate; forming single domaingraphene suspended over the at least one hole.
 2. The method of claim 1,wherein the at least one hole is a plurality of holes of diametervarying from 300 nm up to 1 μm.
 3. The method as defined in claim 1wherein the transition metal layer comprises Ni.
 4. The method asdefined in claim 1 wherein the annealing step includes placing thediamond substrate in a rapid thermal vacuum furnace with a H₂/Ar gasmixture and wherein an annealing temperature is about 800-1000° C. andthe cooling step is performed at a rate of about 600 C./minute.
 5. Themethod as defined in claim 1 wherein a thickness of the transition metallayer is established such that upon completing the dissolving step thetransition metal from the transition metal layer has no trace amount insub-surface regions of the carbon precursor.
 6. A method of forminggraphene on a substrate, comprising the steps of, providing a diamondsubstrate; forming a transition metal layer on the diamond substrate;dissolving the transition metal layer into the diamond substrate by anannealing step having an annealing temperature is about 800-1000° C.;and cooling the substrate, thereby forming a graphene layer from thediamond substrate as a carbon precursor, the cooling performed at a rateof about 600 C./minute; wherein a thickness of the transition metallayer is established such that upon completing the dissolving step thetransition metal from the transition metal layer has no trace amount insub-surface regions of the carbon precursor.
 7. The method as defined inclaim 6 wherein the diamond substrate is selected from the group of (a)single crystal diamond and (b) at least one of: UNCD/NCD/MCD(microcrystalline diamond) thin film diamond deposited on a Sisubstrate.
 8. The method as defined in claim 6 wherein the transitionmetal layer comprises Ni.
 9. The method as defined in claim 6 whereinthe annealing step includes placing the diamond substrate in a vacuumfurnace with a H₂/Ar gas mixture.
 10. The method of claim 6, wherein thesubstrate is heated to the annealing temperature in about 30 s forannealing.